Brief Lives

Bertrand Russell (1872-1970)

Alistair MacFarlane reveals paradoxes in the long life of the third Earl Russell.

Bertrand Russell, third Earl Russell, was born on 18th May 1872 at Cleddon Hall, Monmouthshire, into one of the great political families of Britain. His grandfather, Lord John Russell, the Whig politician and first Earl, who twice became Prime Minister, steered the 1832 Reform Act through Parliament. John Stuart Mill was Bertrand’s godfather, and young Bertie was introduced to Queen Victoria when he was two years old. Russell became a great and innovative philosopher, but he had politics in his genes.

Russell’s mother died when he was two years old, his father when he was three. There were two older siblings, a brother Frank, and a sister Rachel, who died young. Russell and his brother were brought up by their grandparents in Pembroke House, in the middle of Regent’s Park in London. (The house was the gift of Queen Victoria, and had been given in gratitude for Lord Russell’s political services. This was fitting, since, without the Reform Act, Victoria might not have had a throne to sit on.) Here the friendless boy grew up, looked after by a succession of Swiss and German nurses and governesses, and taught at home by a succession of English tutors. He was lonely, unhappy and highly precocious.

At the age of eleven he discovered Euclid, although he was severely disappointed to find that the sublime logical edifice of geometry rested on unprovable, assumed axioms – a hint of things to come. By his own efforts he rediscovered Cartesian geometry, seeing in principle how planetary orbits could be calculated. He read widely, but without overall direction. Although he disagreed with his godfather’s logic, the political ideas in Mill’s On Liberty affected him profoundly.

When Russell went up to Cambridge at the age of eighteen, in his own words, he “entered a new world of infinite delight.” (‘My Mental Development’ in Volume 5 of The Library of Living Philosophers, 1944.) Suddenly he was amongst people who spoke the sort of language natural to him, and when he said what he really thought, “they neither stared at me as if I were a lunatic nor denounced me as if I were a criminal” – unlike his family or tutors. In Trinity College he made lasting friends, and the environment “fitted like a glove.” (Later quotes from ‘Adaptation: An Autobiographical Epitome’ in Bertrand Russell, Portraits from Memory and Other Essays, 1956.) The oppressive and morbid atmosphere in which he had been brought up had paralysed his social development, but he soon became confident, optimistic and self-reliant. His first three years were devoted to mathematics, and the fourth to philosophy. He had found his feet, and never looked back.

On graduating, he had to decide whether to devote himself to philosophy or politics, the latter having been the habitual pursuit of his family since the sixteenth century. In 1894 he married Alys Pearsall Smith, an American Quaker. The family pressures on him remained intense, and it seemed to the young man that not to pursue politics would be an act of treachery. Everything was done to smooth a way for him. The British Ambassador in Paris gave him a job at the embassy. But after a short time the lure of philosophy proved irresistible, and he returned to Cambridge in 1895.

For his Fellowship election to Trinity, Russell submitted a dissertation on the foundations of geometry; and the logical foundations of mathematics absorbed him totally for the next decade. In Principles of Mathematics (1903) he argued that mathematics was simply logic. Then, together with Alfred North Whitehead, a senior fellow [see Brief Lives in Issue 86], he sought to establish this idea conclusively.

As an undergraduate Russell had become increasingly disenchanted with the way in which his lecturers and tutors had presented mathematics. Their lack of logical rigour seemed to reduce it to no more than a bag of tricks designed for the puzzle-solving requirements of the Mathematical Tripos [exams]. His interests shifted to the need to put mathematics on a secure logical basis, and so from maths to philosophy. But the need for a foundation for mathematics was more than a philosophical challenge. Russell craved an absolute certainty which he felt he could only find in this way. For over a decade he laboured mightily with Whitehead on the monumental undertaking to provide mathematics with a secure logical basis. Their work transformed mathematical logic, but it foundered on what has become known as ‘Russell’s Set Paradox’.

Russell and Whitehead’s fundamental logical entity was the set. Most sets are not members of themselves, but some are, such as the set of all non-men (because a set is not a man). The logical iceberg which their philosophical Titanic struck was the question: Is the set of all sets which are not members of themselves a member of itself? This is neither true nor false [see Principia Mathematica]. Thus Russell’s dream of certainty became a nightmare of paradox. After nearly two years, a way was found to patch things up, by defining a suitably restricted class of sets. But irreparable damage had been done, both to the attempt to provide mathematics with an incontrovertible foundation in logic, and to the attempt to satisfy Russell’s craving for certainty. Nevertheless the final result of Russell and Whitehead’s prodigious efforts, Principia Mathematica (1910-1913), was a towering intellectual achievement.

Denied the absolute certainty which he had sought – a rock on which to establish his thinking – Russell’s interests now moved decisively towards realism and semantics. Having found that logic could not be used to spin a web fine enough to ensnare mathematics, he did not abandon logic, but developed an analytical approach that led to what is now called ‘philosophical logic’. Russell thus led a revolt against Idealism, a doctrine fashionable in philosophy at the turn of the twentieth century, and the techniques which he developed established the basis of 20th century analytical philosophy.

Despite an increasingly hectic and complex life, Russell continued to publish extensively, ranging widely over philosophy, sociology and politics. His major philosophical works include: On Denotation (1905), The Problems of Philosophy (1912), Mind and Matter (1925), The Analysis of Matter (1927), and Human Knowledge (1948). He wrote an acclaimed History of Western Philosophy (1945), which gave him a valuable income for the rest of his life, and was awarded the Nobel Prize for Literature in 1950. Russell also spent much time in encouraging the young Wittgenstein [Brief Lives in Issue 87], despite the consequent drain on his emotional resources, and he strongly supported the work which led to Wittgenstein’s acclaimed Tractatus Logico-Philosophicus. Russell developed his own version of the ideas Wittgenstein presented in that book, giving a series of lectures on Logical Positivism in 1918, while Wittgenstein was still in a prisoner of war camp. Wittgenstein claimed that his ideas had been misunderstood and therefore misrepresented, and the relationship between them never recovered.

Russell’s Autobiography, published in three volumes (1967-69), is remarkable for its frankness and objectivity. In it he recounts how, when out riding his bicycle in 1901, he realised that he no longer loved Alys. Telling her this effectively wrecked the marriage. Subsequently he had many passionate relationships, often simultaneously, and most famously with Lady Ottoline Morrell and the free spirit Dora Black. Finding that Dora was pregnant in 1921, he hastily divorced Alys and married Dora six days later. It was, by agreement, an open marriage. Dora had several children by other men, and two children by Russell. Together Dora and Bertrand founded the experimental Beacon Hill School in Sussex in 1927.

They divorced in 1932, and Russell immediately married the children’s governess, Patricia Spence. They had a son who became a prominent historian and a leading Liberal Democrat. This marriage lasted until 1952, and soon afterwards he married Edith Finch, whom he had known since 1925.

During the First World War, Russell was a determined and outspoken advocate of pacifism. An anti-war article he wrote landed him in prison for six months, and he was deprived of his Fellowship at Trinity. However, he regarded the Second World War as a just war, considering totalitarianism a great evil. For the rest of his life he became increasingly involved in political protest and anti-authoritarian and anti-war demonstrations. A passionate opponent of nuclear weapons, he telegraphed both the Kremlin and the White House during the Cuban Missile Crisis: Khrushchev replied, but the telegram to Kennedy was returned unopened.

Russell’s work has had a lasting significance for logic, mathematics, set theory, computational science (theory of types), the philosophy of language, epistemology, and metaphysics. Very few philosophers have had such a lasting effect over so many fields. He gave the inaugural series of Reith Lectures in 1948, was awarded the Order of Merit in 1949 (a high honour in Britain), and continued to be politically active to the end of his long life. One of his last public acts was to issue a condemnation of Israeli aggression in the Middle East.

Russell died of influenza on 2 February 1970 in Penrhyndeudraeth, Wales – the land of his birth, with which his family had been politically associated since the time of the Tudors. His ashes were scattered in the nearby Snowdonia mountains.

No other great philosopher has been so long and so effectively involved in the public domain.

Sir Alistair MacFarlane is a former Vice-President of the Royal Society and a retired university Vice-Chancellor.

Principia Mathematica

The goal of Principia Mathematica was to provide a logically secure foundation for mathematics. The basis of Russell and Whitehead’s theory of numbers was Set Theory. The number four, for instance, means the set of all sets with four elements. But part-way through this massive project, Russell discovered a fundamental paradox in set theory which shook the foundations of their edifice before they had even finished building it.

Russell’s Paradox is the question: ‘Is the set consisting of {all sets which are not members of themselves} a member of itself?’ This is a paradox because if this set is not a member of itself, then it is, and if it is a member of itself, then it’s not… Russell worked for two years to find a way around the problem and eventually the project was completed, but the foundations never looked as secure as once hoped.

Russell also pioneered the field of philosophical logic. At the beginning of the Twentieth Century, philosophers aspired to represent the propositions of ordinary language in a logically rigorous way. Russell was one of a number of philosophers involved in formulating a symbolism for this purpose. It was hoped that this would enable ordinary-language propositions to be expressed in a form that would allow them to be manipulated in the sort of way that mathematicians manipulate equations. Nowadays, however, it is recognised that ordinary language use is too flexible, nuanced and equivocal to be easily reducible to logical symbols, and manipulated in a straightforward logical/mathematical way.

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